An alternative sensitivity for state-space digital filters

Abstract

In this paper, a new sensitivity measure for state-space digital filters is proposed. The new measure is a modified form of Tavsanoglu and Thiele's measure, but the new one has three advantages: (1) it is more precise than Tavsanoglu and Thiele's measure when the state-space realizations of a digital filter contain 0 and /spl plusmn/1 coefficients; (2) it can be used to explain why the sparse Schur and Hessenberg realizations will give a better actual sensitivity performance than the corresponding fully parametrized optimal realizations; (3) it is equal to the global roundoff noise gain G=tr(QW)+/spl gamma/ obtained by Hwang under the dynamic constraint.